{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 24\n",
    "\n",
    "# 统计视角下的回归\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f440e5d-4d9e-46f4-a646-a1126a43a52a",
   "metadata": {},
   "source": [
    "在这段代码中，我们首先定义了一个用于可视化鸡和兔子数量关系的函数。然后生成两个数组，分别表示不同实验中鸡和兔子的数量。通过计算这些数量的标准差和相关系数，我们得到了变量之间的关系。接着，利用线性回归模型计算出最佳拟合线的斜率$a$和截距$b$。\n",
    "\n",
    "具体而言，斜率$a$的计算公式为：\n",
    "\n",
    "$$\n",
    "a = \\frac{\\text{Cov}(X, Y)}{\\text{Var}(X)}\n",
    "$$\n",
    "\n",
    "其中，$\\text{Cov}(X, Y)$是鸡和兔子数量之间的协方差，而$\\text{Var}(X)$是鸡数量的方差。截距$b$的计算则使用了均值：\n",
    "\n",
    "$$\n",
    "b = \\bar{Y} - a \\cdot \\bar{X}\n",
    "$$\n",
    "\n",
    "其中，$\\bar{Y}$和$\\bar{X}$分别是兔子数量和鸡数量的均值。\n",
    "\n",
    "接着，使用散点图和回归线展示了鸡的数量与兔子的数量之间的关系。回归线的方程为：\n",
    "\n",
    "$$\n",
    "y = ax + b\n",
    "$$\n",
    "\n",
    "其中$y$是兔子的数量，$x$是鸡的数量。最后，使用`sklearn`库中的`LinearRegression`模型对数据进行拟合，并输出计算得到的斜率和截距，以便与之前的结果进行比较。\n",
    "\n",
    "通过这种方式，代码不仅展示了如何计算线性回归参数，还通过可视化方式帮助理解不同变量之间的关系，尤其是在动物数量的生态学研究中，这种分析方法可以揭示它们之间的相互影响。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5628ab47-c9dc-49c8-90e1-48d0085c29b4",
   "metadata": {},
   "source": [
    "## 导入必要的库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "51279352-4d30-4867-addf-a744590d28f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算\n",
    "import seaborn as sns  # 导入Seaborn库，用于绘制回归线\n",
    "import matplotlib.pyplot as plt  # 导入Matplotlib库，用于绘图"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "952b55f8-78b6-49eb-8969-bc8c75f19573",
   "metadata": {},
   "source": [
    "## 定义图形装饰函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1fc20917-4444-463d-964c-a51294ce42df",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fig_decor(ax):  # 自定义函数，用于装饰图形\n",
    "    plt.xlabel('$x$ (number of chickens)')  # 设置x轴标签，表示鸡的数量\n",
    "    plt.ylabel('$y$ (number of rabbits)')  # 设置y轴标签，表示兔的数量\n",
    "    plt.axis('scaled')  # 设置坐标轴比例相同\n",
    "    ax.set_xlim([0, 120])  # 设置x轴范围为[0, 120]\n",
    "    ax.set_ylim([0, 80])  # 设置y轴范围为[0, 80]\n",
    "    plt.xticks(np.arange(0, 120 + 1, step=10))  # 设置x轴刻度，每10为一档\n",
    "    plt.yticks(np.arange(0, 80 + 1, step=10))  # 设置y轴刻度，每10为一档\n",
    "    plt.minorticks_on()  # 开启次刻度显示\n",
    "    ax.grid(which='minor', linestyle=':', linewidth='0.5', color=[0.8, 0.8, 0.8])  # 设置次刻度网格线样式\n",
    "    ax.spines['top'].set_visible(False)  # 隐藏顶部坐标轴\n",
    "    ax.spines['right'].set_visible(False)  # 隐藏右侧坐标轴\n",
    "    ax.spines['bottom'].set_visible(False)  # 隐藏底部坐标轴\n",
    "    ax.spines['left'].set_visible(False)  # 隐藏左侧坐标轴\n",
    "    ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 设置主刻度网格线样式"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70fe6e9e-779f-43c6-8642-2713100ce691",
   "metadata": {},
   "source": [
    "## 定义鸡和兔的数量数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "423b614d-733b-491f-a057-c6745012dc11",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_chickens = np.array([32, 110, 71, 79, 45, 20, 56, 55, 87, 68, 87, 63, 31, 88])  # 鸡的数量数据\n",
    "num_rabbits = np.array([22, 53, 39, 40, 25, 15, 34, 34, 52, 41, 43, 33, 24, 52])  # 兔的数量数据"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeb8279d-4fee-418d-afca-ad493e537435",
   "metadata": {},
   "source": [
    "## 计算统计量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ad7699e9-8b6f-4bcd-8be9-c984b8e9aed3",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_X = num_chickens.std(ddof=1)  # 计算鸡的数量的标准差\n",
    "sigma_Y = num_rabbits.std(ddof=1)  # 计算兔的数量的标准差\n",
    "rho_XY = np.corrcoef(num_chickens, num_rabbits)[1][0]  # 计算鸡和兔数量的相关系数\n",
    "mean_X = num_chickens.mean()  # 计算鸡的数量的均值\n",
    "mean_Y = num_rabbits.mean()  # 计算兔的数量的均值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b915140-7055-42f4-8b36-01ebbc95c2e4",
   "metadata": {},
   "source": [
    "## 计算回归系数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "79e18e77-c5ed-45ac-b761-7ca6ad4698f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = rho_XY * sigma_Y / sigma_X  # 根据公式计算斜率\n",
    "b = -a * mean_X + mean_Y  # 根据公式计算截距"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cc19bcf-d664-4c2f-b1f4-226c25b1383d",
   "metadata": {},
   "source": [
    "## 打印斜率和截距"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d1b20ed0-3330-4b8a-aee7-4fbdb01a5c58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Slope, a ===\n",
      "0.44338807260155577\n",
      "=== Intercept, b ===\n",
      "7.964131374243731\n"
     ]
    }
   ],
   "source": [
    "print('=== Slope, a ===')  # 输出斜率的标题\n",
    "print(a)  # 输出斜率的值\n",
    "print('=== Intercept, b ===')  # 输出截距的标题\n",
    "print(b)  # 输出截距的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "014ff604-2e4f-4721-821e-0a2c952787e0",
   "metadata": {},
   "source": [
    "## 绘制回归图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a54c2207-038f-4002-bcf3-173285adb8b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.linspace(0, 120, 20)  # 创建x轴的取值范围"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "91421f93-f9b0-43e8-a5fb-c41d95352335",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建一个新的图形和坐标轴\n",
    "sns.regplot(x=num_chickens, y=num_rabbits, ax=ax, truncate=False, line_kws={\"color\": \"red\"})  # 使用Seaborn绘制回归线\n",
    "plt.plot(mean_X, mean_Y, marker='x', markerfacecolor='r', markersize=12)  # 在均值点位置绘制标记\n",
    "fig_decor(ax)  # 调用图形装饰函数，设置图形样式"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "661f6094-20a9-4b80-ae4a-29fddd5b2c10",
   "metadata": {},
   "source": [
    "## 使用sklearn计算线性回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b10efca5-cee8-426c-a123-e38eb8bf8bbf",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression  # 导入sklearn的线性回归模块"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "680ed6b5-bb12-4670-b239-a18e30677678",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = num_chickens.reshape((-1, 1))  # 将鸡的数量数据重塑为列向量\n",
    "y = num_rabbits  # 定义兔的数量数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a4ad67d1-4251-4f0a-80e0-87e713acf5c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x, y)  # 拟合线性回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c2a28b69-5d91-4ec5-9596-192ddd92c123",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope, a: [0.44338807]\n",
      "Intercept, b: 7.964131374243742\n"
     ]
    }
   ],
   "source": [
    "print('Slope, a:', model.coef_)  # 打印模型的斜率\n",
    "print('Intercept, b:', model.intercept_)  # 打印模型的截距"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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